Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 168: 47e

$0.25$ is a meaningless value for t as it results in $\tan 0.5\pi$ which is undefined.

We substitute $t=0.25$ in the equation and then solve for $d$: $d=4\tan 2\pi t$ $d=4\tan 2\pi (0.25)$ $d=4\tan (2\pi \times0.25)$ $d=4\tan 0.5\pi$ Since $\tan 0.5\pi$ is undefined, no further simplification is possible. Therefore, $0.25$ is a meaningless value for t as it leads to $\tan 0.5\pi$ which is undefined.